Thay're not saying that gravity waves are creating the signals. What they are saying is that if gravity waves are creating any signals at all, the size of the signals being measured limits the possible size of the gravity waves to smaller than a certain size. It is putting an upper bound on the possible size of gravity waves. This is important, because the previously determined upper bound on gravity wave size was 9 orders of magnitude bigger than it is now that we have these experimental results.

What "other things"? Electromagnetism is the only thing that has comparable speed to gravity waves, and unlike gravity waves, it only penetrates Earth-sized solid matter with exponential falloff at short distances. Forget possible seismic causes for the kind of measurements they must be looking for. Just recalling my high school physics 101, you know...

Also, from TFA:

Gravitational waves are the last untested prediction of Albert Einstein's General Theory of Relativity.

I'd argue that this is debatable, seeing that we've already measured the decay of at least one binary pulsar that wonderfully corresponds to the predicted gravity-wave-mediated energy loss.

What they did is say is basically "We now have a detector 10^9 times more sensitive, which is capable of detecting gravitational waves up to 10^9 times smaller than previous detectors, if there are waves. We didn't see any waves with this detector. Therefore if they exist, they are smaller than what our new detector can detect".

In other words, if there are gravitational waves, they are smaller magnitude than they are able to detect with the new detection system. This doesn't rule them out, it just blacks out a potential energy/amplitude range in which they might have existed before nothing was seen in that search band.

They've more or less reduced the probability set, and pissed in a number of esoteric theories cheerios, but not done a lot else to prove or disprove gravity waves.

It's the difference between having to look for a lost item in an entire warehouse, or having to look for it in a crackerjack bix sized area of the warehouse - albeit it'll take a lot more expensive and redesigned equipment to even look in part of the crackerjack box.

Frankly, if we threw 4 ten ton spheres into relatively deep space (e.g. solar orbit), arranged them at the vertices of a tetrahedron, and then used laser interferometry between the spheres, and then threw another ten ton sphere across the solar system at a non-trivial speed, and through the tetrahedron, not intersecting a face or the body center, we could pretty much say once and for all if there were gravity waves or not, based on delay (or non-delay) of the effect of the moving sphere being "not there, then suddenly there, then suddenly not there", at least to about 1/2 the wavelength used by the interferometers (hence the need for a "non-trivial speed" for what is, in effect, a gravitational probe inserted into the system, to do the experiment).

Doing the more or less definitive experiment would be expensive (as in "on the order of the cost of the LHC").

The two used much different frequency regimes. The Stanford paper [stanford.edu] looked for waves with periods of 30 minutes to 24 hours. The one in the article looked for waves with periods of 1 to 20 seconds.